Upon taking the helm of Valeant Pharmaceuticals International Inc., Joseph Papa promised to start a “new chapter” at the struggling company. But Wall Street is questioning whether the man hired to effect change can succeed after drawing from a playbook similar to Valeant’s at his previous company.

While piloting Perrigo Co., Mr. Papa took steps akin to those that put Valeant on the hot seat. He raised prices of prescription drugs—by more than many rivals did—including boosting lice treatment permethrin and a steroid...